Tannakian duality for affine homogeneous spaces

Abstract

Associated to any closed quantum subgroup $G\subset U_N^{+}$ and any index set $I\subset \{1,\dots ,N\}$ is a certain homogeneous space $X_{G,I}\subset S_{\mathbb{C},+}^{N-1}$, called affine homogeneous space. We discuss here the abstract axiomatization of the algebraic manifolds $X\subset S_{\mathbb{C},+}^{N-1}$ which can appear in this way, by using Tannakian duality methods.

arXiv comment12 pages